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Estonian Math Competitions 2005/2006

Source: Final Round Grade 11 Pro 3

July 30, 2008
inductionnumber theory unsolvednumber theory

Problem Statement

The sequence (Fn) (F_n) of Fibonacci numbers satisfies F_1 \equal{} 1, F_2 \equal{} 1 and F_n \equal{} F_{n\minus{}1} \plus{}F_{n\minus{}2} for all n≥3 n \ge 3. Find all pairs of positive integers (m,n) (m, n), such that F_m . F_n \equal{} mn.
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